The goal of the research project is to carry out an extensive investigation of several areas of statistical methodology for the design and analysis of biomedical studies, applicable to various areas of health research, especially cancer clinical trials and epidemiology. The research falls into four main categories: (a). Evaluation of adaptive group sequential clinical trials. This methodology permits design modifications in mid-course, while preserving the Type I error. The changes may be caused by information either internal or external to the trial. We will emphasize procedures based on the sufficiency principle so that efficiency (power) is maximized. We will develop a theory of optimal adaptive tests and produce a "catalog" of conventional non-adaptive designs that are easy to implement yet are almost as efficient. We investigate the related topic of strategies of accelerating the process of staged development of new therapies. (b). Statistical design and analysis of studies that involve clustered data. These arise, for example, in familial aggregation, teratology and cluster randomized trials. We concentrate on binary, continuous, survival and multivariate mixed type endpoints from clusters of unequal sizes. Responses are exchangeable, possibly after inclusion of covariates, which may act at cluster- or individual-level. We develop both likelihood based and Bayesian inferences procedures, the latter utilizing MCMC techniques. Inclusion of higher order interaction terms permit examination of the complexity of the correlation structure. (c). Design and evaluation of dynamic diagnostic indices that may be used as tools for monitoring pros pectively for onset and stages of disease using accumulating serial biomarker measurements. We propose the use of hidden continuous time Markov chain models for longitudinal biomarker data and apply reversible jump MCMC methods. A particular application is to PSA as a marker for stages of prostate cancer. (d). Various other topics that arise in analyses and meta-analyses of clinical trial data.